Generalized Parametric Intuitionistic Fuzzy Measures Based on Trigonometric Functions for Improved Decision-Making Problem

Generalized Parametric Intuitionistic Fuzzy Measures Based on Trigonometric Functions for Improved Decision-Making Problem

Pawan Gora, Vijay Prakash Tomar
Copyright: © 2023 |Pages: 26
DOI: 10.4018/IJDSST.323444
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Abstract

Information theory is the study of collecting, storing, and sharing digital information. It is a nexus of disciplines such as statistics, computer science, statistical mechanics, and probability theory. This study pertains to intuitionistic fuzzy sets theory, which is a substantial component of fuzzy set theory. Nonetheless, the motive of the study is to find vague information intuitionistic fuzzy entropy measures. The authors are extend the parametric intuitionistic fuzzy entropy measures by using trigonometric functions and investigate the difference between proposed study & existing entropy measures. Furthermore, discuss the significance analysis and authenticity of the proposed study. It concludes that the proposed measure could be a good perspective for decision-making problems. Using a suitable illustration, the applicability of the proposed study has been demonstrated. Depict the graph of proposed and existing entropy measure together with their average measure. Additionally, these estimations enhance the study of information theory and produce superior information.
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1. Introduction

The communication genrally exist with transferring of information from one source to other. According to the information theory, the communication process is a crucial aspect of information collection, as it is the source of authentic information. Shannon (Shannon, 1948) established probabilistic entropy for continuous and discrete probability distributions. Analogues to the concept of probability theory, (L.A.Zadeh, 1965) describe the fuzzy sets (FSs) theory and introduced fuzzy entropy on fuzzy sets. Afterwards, (K. T. Atanassov, 1986) invented the intuitionistic fuzzy sets (IFSs) theory, which raised the study of information theory, it facilitates the investigation of information theory. Atanassov and Gargov (1989) developed the study of interval valued intuitionistic fuzzy sets (IVFSs) which is the extension of intuitionistic fuzzy sets. In this present study, the authors are analyze the non-membership function beyond the membership function and construct the measures to determine the uncertain information. It attained the considering degree values between zero and one, corresponding to every point of the universe of discourse. The intuitionistic fuzzy set theory is an extensive study of (L.A.Zadeh, 1965) fuzzy set theory. Under this environment, IFSs entropy deals with the study of uncertain information. Burillo & Bustince (1996) reveal the concept of IFSs entropy measures for uncertainty and found the relationship between IFSs and IVFSs. Gau and Buehrer (1993) discussed the idea of vague sets, which is based on the notion of fuzzy set theory. Szmidt & Kacprzyk (2001) drew out the postulates De Luca and Termini (1971) for IFSs entropy measure and developed a non-probabilistic IFSs entropy measure based on the geometrical interpretation of IFSs. Here, few complexity is arise in the present communication, therefore, some new entropies were created. This overcomes the past study for finding the relevant results of uncertainty. On the basis of the pioneering work of (A. De Luca and S. Termini, 1971), (Vlachos & Sergiadis, 2007) generalised the IFS entropy measure. Subsequently, the several authors overgeneralize the different types of entropies in the IFSs environment. Zhang & Jiang (2008) additionally enhanced (A. De Luca and S. Termini, 1971) entropy on the IFSs environment. On this concept, Verma and Sharma (2014) developed the IFSs entropy measure based on (N. R. Pal & Pal, 1989) fuzzy entropy. Afterwards, numours authors are suggested several kinds of entropy for IFSs and having the applicability with their relevance. Numerous authers were introduced the different types of IF entropy measure and they have investigated some shortcoming related to to developed study. Wei et al. (2012) and Wang et al. (2012) suggested an IF entropy measure employing the cosine function and cotangent function, respectively.

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